System for detecting, tracking, and reconstructing signals in spectrally competitive environments

ABSTRACT

A system applicable to acoustic, seismic, electromagnetic, hydrodynamic, and shock waves utilizing a map between signal time series and signal vectors defining the mathematical wave field model characterizing the signal&#39;s wave field. This map is developed from wave models relating field values to those on surfaces and corresponding uniqueness theorems. The system should allow for improved resolving power in bearing and elevation for discrimination of sources; detection and direction finding for signals below the average background level; detection based upon resolving power and signal vector characteristics rather than signal to noise ratio; reconstruction of signals of resolved sources for their transmitted information content; and multiple modes of operation. Adaptive incorporation of known undesired signals into the noise background and/or treatment of asymmetric background noise fields is permitted through use of a noise metric-based map yielding signal direction in the presence of diffraction effects.

This is a continuation of application Ser. No. 11/200,264, filed Aug. 9,2005, the entirety of which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to a system for three dimensional multiplesignal tracking and reconstruction for use in connection with search andrescue, surveillance, storm and severe weather alerting, animal and birdmigration, subsurface mapping, anti-terrorism, conventional warfare,etc.

Analog beamforming and antenna steering using loop, parametric and/orphased arrays, are methods employed for direction finding of acousticand electromagnetic waves belonging to quasi-continuous signals. In oneapproach, a directional antenna (such as a parasitic array or loopantenna) is rotated towards the source for maximum reception. Thedetector may be a single receiver, as in the case of electromagneticdevices, or might be human ears receiving the output of two microphonesmounted in the centers of large megaphones. The antenna's ‘beam’ couldalso be steered at a given frequency of operation by artificiallyintroducing appropriate time delays into the detected signals fromdifferent antenna elements. These analog forms of beamforming wereemployed in World War II (radar and acoustics), for tracking aircraftand for transmitter hunting, and traditionally by radio amateurs inhunting hidden transmitters in practice for emergencies for sport, andfor the elimination of undesired signals.

The time of arrival method has also been applied to locating sources ofshort duration signals, such wave pulses generated by earthquakes,shocks, blasts from explosions, cell phones, etc. Time of arrivaltechniques generally seek absolute and arrival time differences betweensignal arrivals at antenna transducer elements. Such systems typicallyobtain information from two or more antennas to obtain directions ofincoming signals and employ triangulation techniques to estimate pointsof origins.

For quasi-continuous signals, certain beamforming and beam steeringmethods use fixed antenna arrays of transducer elements and digitalsignal sampling and processing to convert signal conditioned antennaoutput signals into digitized time series. These methods generally donot require antennas to be rotated, but instead typically make use ofsecond order statistical functions obtained from cross-correlations andcross-spectral densities of time series of the different antennaelements. The second order statistical procedures allow for thedetermination of preferred signal directions and signal power spectra.Artificial channel time delays using digital processing can be used tonumerically steer “antenna beams” and can also incorporate antenna beammodifications for adaptive processing and removal of undesired sources.

In contrast, the present system is based upon the creation andmanipulation of signal vectors providing for the construction ofmathematical models of physical wave fields at or in the vicinity of theantenna.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing, as well as other objects of the present invention, willbe further apparent from the following detailed description of thepreferred embodiment of the invention, when taken together with theaccompanying specification and the drawings, in which:

FIG. 1 is a block diagram of a system constructed in accordance with thepresent invention for a composite acoustic, electromagnetic, and seismicantenna array with self calibration capability;

FIG. 2A is a schematic representation of a spherical microphone antennaconstructed in accordance with the present invention supporting signalvector processing;

FIG. 2B is a perspective view of a cylindrical three dimensional (3D)acoustic array constructed in accordance with the present inventionsupporting signal vector processing;

FIG. 3A is a perspective view, with parts cut away, of a charge densitysampled electromagnetic spherical shell antenna constructed inaccordance with the present invention supporting 3D signal vectorprocessing;

FIG. 3B is a partial perspective view of a capacitive transducerconstructed in accordance with the present invention for samplingelectromagnetic spherical shell antenna surface charge densities atpoints on the surface;

FIG. 4A is a perspective view of a current-sampled electromagnetic 3Dvertical whip antenna constructed in accordance with the presentinvention with ring sub array capable of supporting 3D signal vectorprocessing for elevation angle and bearing determination;

FIG. 4B is a plan view of a sub array ring element constructed inaccordance with the present invention of the antenna in FIG. 4A, whichcan also serve as a planar two dimensional (2D) “bicycle wheel” antennawhen the antenna of FIG. 4A operates in planar mode, or as a stand aloneantenna operating as a 3D antenna in planar mode;

FIG. 4C is a partial perspective view of an inductive transducer formeasuring the electric current at points along the sub array ringelement of FIG. 4B and the rings of FIG. 4A;

FIG. 5A is a schematic representation of a prolate spheroidal shellantenna constructed in accordance with the present invention havingcapacitive and/or inductive transducers supporting 3D operation, planarmodes of operation, signal vector processing and/or possiblyreconstruction of electromagnetic signals; and with microphone and/orhydrophone transducers, could also operate as a submerged and/or towedantenna for scanning sonar and for tracking applications;

FIG. 5B is a schematic representation of a cylindrical shell antennaconstructed in accordance with the present invention having capacitiveand inductive transducers supporting 3D operation, planar modes ofoperation, signal vector processing and/or possibly reconstruction ofelectromagnetic signals; and with microphone and/or hydrophonetransducers could also operate as a submerged and/or towed antenna forscanning sonar and tracking applications;

FIGS. 5C and 5D are a set of partial perspective views of capacitive andinductive transducers, respectively, constructed in accordance with thepresent invention for use on the antennas shown in FIGS. 3-5B formeasuring electric charge and current vector components at selectedpoints on electromagnetic shell antennas;

FIG. 6 is a perspective view of an acoustic “tree” array configurationconstructed in accordance with the present invention and designed toaccount for the coupling of direct and reflected waves by the surface onwhich the antenna is mounted and supporting 3D signal vector processing;

FIG. 7 is a schematic representation of electromagnetic and acousticarrays of the types depicted in FIGS. 2-5B mounted on a vehicle fordeployment in an urban environment and illustrating the application ofthe present invention to locate snipers and cell phones when used with atraceback program;

FIG. 8 is a schematic representation of acoustic and electromagnetic(EM) high density array deployed in accordance with the presentinvention on a vehicle and capable of determining the direction ofincoming fire, of tracking helicopters and/or vehicles, and fordirection finding and tracking of electromagnetic sources such asVHF/UHF hand held radios and cell phones;

FIG. 9 is a schematic representation of farmhouse or barn mounted arraysconstructed in accordance with the present invention for detection ofsevere storms, for providing early warning for tornadoes andthunderstorms, and for announcing the arrival of visiting vehicles;

FIG. 10A is a schematic representation of an active towed transducerarray constructed in accordance with the present invention forapplication as a scanning sonar to 3D image of submerged objects and forallowing observation of objects as the towed transducer arrayapproaches, passes, and departs;

FIG. 10B is a schematic representation of a fixed bottom-mounted orsurface-suspended cylindrical hydrophone array constructed in accordancewith the present invention for monitoring and tracking of shipping,internal waves, and/or tsunamis which may employ hydrophones, geophones,and/or vector magnetometers;

FIG. 11A is a schematic representation of a bottom-mounted hydrophone,3D tree or spherical array constructed in accordance with the presentinvention for harbor security applications, having both passivedetection and tracking capability (including those capabilitiesreferenced in FIG. 10B) and small boats and swimmer delivery vehicles,depending upon the antenna size and configuration;

FIG. 11B is a schematic representation of a swimmer delivery vehicle anda bottom-mounted cylindrical array constructed in accordance with thepresent invention for applications as referenced in FIG. 10B, and withapplicability to small boats and swimmer delivery vehicles, dependingupon the antenna size and configuration and type of transducer(magnetic, hydrophone, vector magnetometers, etc.);

FIG. 12 is a schematic representation of a mountain deployment of athree dimensional acoustic spherical array constructed in accordancewith the present invention of the type shown in of FIG. 2, havingbearing and azimuth capability for traffic and/or projectile and/oraircraft tracking and monitoring, and for location of sources, using aincident ray traceback program;

FIG. 13 is a schematic representation of an active and/or passiveseismic array constructed in accordance with the present inventionconsisting of geophones mounted at the end of bore holes drilled intothe mountainside, for permitting mapping and/or monitoring ofunderground facilities;

FIG. 14 is a schematic representation of a combined seismic and/oracoustic array constructed in accordance with the present inventiondeployment for tracking wheeled vehicles, shock waves, and helicopters;

FIG. 15 is a schematic representation of calibration electronicsconstructed in accordance with the present invention showing a signalgenerator, coupling to transducers, amplifiers, A/D converters, andprocessor;

FIG. 16 is a perspective view of a single channel acoustic transducerdriver constructed in accordance with the present invention for anoperator-supported calibration, for which calibration can be carried outone channel at a time;

FIG. 17 is a plan view of a multiple channel acoustic transducer driverconstructed in accordance with the present invention for simultaneousmultiple channel calibration;

FIG. 18 is a schematic representation of an example dual purpose sevensensor acoustic and/or seismic sensor array constructed in accordancewith the present invention with supporting signal conditioning unit,sample geophone, microphone, and computer for in-field processing; and

FIG. 19 is a schematic representation of a transducer positioncalibrating method of the present invention using a field survey andapplicable to large scale antennas whose transducer locations may havebeen altered by environmental events.

SUMMARY OF THE INVENTION

Generally, the present invention includes a method and apparatus fordetermining selected information from signals contained in a physicalwave field, the properties of the physical wave field being detectableover three spatial dimensions and a temporal dimension, and the methodincluding characterizing the physical wave field by a signal vectorproviding a mathematical model of the physical wave field, anddetermining the selected information from the signal vector.

The necessary equations, theory, and computational tools required forconstructing embodiments of the present invention for the differentphysical wave types are historical and well known and can be establishedusing the following texts (which are incorporated herein by reference):Stratton, Electromagnetic Theory, 1941 Chap 9; Jackson, ClassicalElectrodynamics, 1962 Chapter 16; Roger G. Newton, Scattering of Wavesand Particles, 1966; (Jenkins and White, Fundamentals of Optics, 1957);Thorne Lay & Terry C. Wallace, Modern Global Seismology, 1995; andOppenheim and Schafer, Digital Signal Processing, 1975; Mathworks,Matlab and Signal Processing Toolbox (User's Guides), 1998; Roman,Theory of Elementary Particles, 1961. As a consequence the details ofthese theoretical notions, equations, and the standard mathematicaltools (Mathworks) are not discussed in detail herein.

The general natures of the approaches of the present invention areapplicable to linear physical wave types or those which can besufficiently treated as linearized waves. Because of the large number ofapplications of the invention to different physical media and wavetypes, for the sake of brevity, illustration of specific applications ofthe preferred embodiment are limited herein to several demonstrativeacoustic and electromagnetic applications, and it is to be understoodthat the present invention is not to be limited to the applications andembodiments disclosed herein.

The conceptual basis for the present invention lies in properties ofsolutions to scalar and vector field wave equations describing physicalwave propagation in different physical media and/or in the fieldsinduced by such propagating waves in certain material media. Themathematical models chosen determine the available information. Thechoice of which physical wave fields are of interest, the propagatingwave and/or the waves it induces on surfaces, depends upon whattransducers are employed and what is required to attain the desiredselected information in the given situation. Under proper circumstancespropagating wavefields in the vicinity of a spatial surface aredetermined by sufficient knowledge of wave fields and their derivativeson that surface over some time interval (see Jackson or Stratton).Kirchoff Surface-Integral representations provide such connections (thetreatment of diffraction is such an example) and so can the waveequation itself (with sufficient knowledge of the field along thesurface power series expansions can be defined to define themathematical model in the vicinity of the surface). With these cases,more extensive selected information can be obtained. In other cases, theability to construct a mathematical model on the surface itself maysuffice. Whatever the choice for selected data, data collection of bandlimited signals through discrete spatial and temporal sampling usingproperly selected transducers placed along such a surface according towell understood criteria can provide the required information, as theNyquist sampling theorem shows. The signal vector is either a collecteddata set containing such required sample information or the equivalent,and therefore contains all the information obtainable from the chosenmathematical model. The selected data, considered already established asobtainable from the field, can be extracted then from signal vectors orthe chosen wave fields through the data reduction procedures describedbelow.

Depending on the nature of the embodiment's antenna, what is beingsampled via data collection, the choice of transducers, and the natureof desired selected data, signal vectors can characterize physical wavefield fluctuations and/or fluctuations in physical “charge” and“current” density fields on surfaces. The latter can arise inelectromagnetism. Thus, the signal vector characterization of anincoming wave field can be indirect. The type of signal vector for themost extensive selected information is that dictated by the proceduresfor mathematical wave field model determination in the antenna vicinity,as described above, for knowledge of the most complete description ofthe propagating wave implies knowledge of the most complete information.

The present invention includes, in certain embodiments, systems andmethodologies using antenna arrays of transducer elements, together withelectronic signal processing hardware, signal conditioning units, signalprocessing software, and reporting electronics. The present inventionincludes a method of deriving signals obtained from properly configuredantenna elements (transducers or sensors) which convert acoustic,seismic, fluid dynamic, electromagnetic and/or electric charge orcurrent density wave fluctuations into fluctuating voltages or currents.These signals are amplified and filtered as necessary, and thendigitized. The resulting time series of the signals constitute a signalvector providing for the construction of a mathematical representationof the physical wave chosen over the bandpass of interest. The signalvector is cast in representation or form suitable for attainment ofdesired selected information. The signal vector is then manipulated fordesired selected data and/or to obtain the signal vectors characterizingresolved sources of incoming signals. A reversal of the process providesfor the construction of a mathematical model for the signals of resolvedsources using their individually characterizing signal vectors, fromwhich the information content they carry can be determined throughdigital signal processing and/or through proper digital to analog(“D/A”) conversion and demodulation.

Pre-constructed libraries of directional and/or modeling signal vectorsand the superposition principle enable the determination of desiredsignal information from data processing algorithms. In essence, the goalof being able to approximately construct the individual signals ofresolved sources of interest as they would be received at the antenna,as if each such resolved source was the only signal present, serves asthe most basic design criteria for embodiments of the present inventionoperating at the highest level. The path to the goal permits theincorporation of new techniques for the extraction of selectedinformation (including that of detection, tracking, and modulationcontent) and the development of new criteria for when such informationis obtainable. However, the system of the present invention can operatewithout reaching the above-stated goal in the event of partial hardwarefailure or breakage, when conditions and desired selected data allow arelaxation of system configuration constraints, or when the chosenmathematical model is not necessary for the attainment of certainselected information.

There are additional fundamental application independent notionsunderlying the concept of the apparatus or invention. One such notion isthat hardware/software/processor configurations and the dimensionalityof the vector space in which the signal vectors are defined are coupledto the resolving power specifying the ability to differentiateneighboring signals having identical frequencies. Yet another is thatantenna sensors can be configured and sampled such that for a givenfrequency bandpass their time series constitute sufficient data to allowdetermination of a signal vector representing the incoming field.Another is that different equivalent representations for a signal vectorcan be chosen, such as those (but not limited to) of the temporal,frequency, and partial wave domains, the choice being applicationdependent. Another fundamental notion is that signal vectors of anydomain can be linearly and quasi-linearly manipulated for noisereduction and for the attainment of selected information, including butnot limited to, that for detection, tracking, and the classification ofmultiple spectrally competitive sources. The superposition principleapplies to signal vectors as well as to the wave fields. Another is thatthe library element signal vectors of preconstructed libraries can beused to construct the individual signals of resolved sources, and thatthose of overlapping data set time segments can be merged to provide fordetermination of the information content of such signals within theoperating bandpass. However, certain elements of desired selectedinformation may not require complete construction of the signal vectorsof each source making up the sampled signal vector.

Different applications of the invention to different wave processesrequire certain changes in hardware components. For example, foracoustic waves in air, microphones could be employed as antennatransducer elements. For acoustic waves in water, hydrophones could beemployed, and for seismic waves, the antenna elements would be geophonesor vector magnetometers, as would also be the case for tsunamis. Forelectromagnetic waves, inductors could be employed or capacitors mountedon or in metallic surfaces. For oceanic internal waves, the transducersmight be thermistors and/or magnetometers. Correspondingly and dependingupon wavelength and frequency, different signal conditioning and dataacquisition units could be used. When necessary, a single mixer may beused to simultaneously lower the frequency of the incoming signals onall channels so that the relative phase and amplitude characteristics ofthe signals of antenna sensor elements are preserved and samplingrequirements reduced. The construction of a signal vector requiresproper choices for antenna sensor placement and configuration, thefrequency bandpass to be sampled, computational word size, and themechanism for determining the signal vector of a chosen representationjointly typically define an embodiment of the present invention. Howevergiven an application, once the signal vector has been determined, theprocedures for computation of selected information are nearlyindependent of the physical type of application. The possibleembodiments of the invention include composite systems capable ofsimultaneously handling all three classes of physical phenomena, as wellas a data reporting system possibly using the utility's antennastructure as part of a microwave or RF transmission remote reportingsystem.

Scalar products between signal and library vectors and constructs of thelatter provide for classes of selected information, depending upon thesignal to noise ratio and the system resolving power. The identificationand detection process also provides bearing and elevation angles ofindividual sources. Multiple source tracking and differentiation isbased upon the resolving power of the embodiment. An adaptive noisebased metric tensor characterizing the environmental noise backgroundredefines scalar products to provide for the adaptive removal ofunwanted and interfering sources and a map between apparent and trueestimates for directions of incoming signal waves, alleviating a beammaintenance problem found with adaptive beamforming approaches. Thelinear nature of the physical wave field to signal vector mathematicalmap enables signal enhancement through signal vector averaging and theattainment of relatively high resolving power through use of highelement density arrays and/or a consequent reduction in numericalprocessing demands.

The system can incorporate use of digitized contour maps of theenvironment. Such digitized data permits incoming signal directions tobe traced back to their points of origin when such tracebacks intersectphysical surfaces characterized in digitized contour maps. In this way,range and source location can be determined from individual antennas.When antennas large enough to measure wavefront curvature are employed,and wavefront curvature is incorporated as a library category, range canalso potentially be determined. When neither of these procedures can beutilized, source range can be determined from triangulation techniquesusing more than one system of the present invention with baselines ofproper length, while Doppler observations can be used to estimatetrajectory directions and closest points of approach.

The system can incorporate calibration and self-testing for verificationof performance criteria. The self calibration and self-testingcapabilities allow for automatically switching to alternate modes ofoperation, with perhaps some reduction in signal detection and resolvingcapability, should some signal channels become damaged or disconnected.

Using subsets of predetermined signal vector libraries, threedimensional systems can be operated in two dimensional modes whenincoming signals have their wave propagation vector in a common plane.With a 3D system, this can be done in any plane. Thus, with the systemof the present invention, optimum performance may be obtained for wavespropagating parallel to the surface of the ground even if the antennamast is not vertical. The 3D algorithms can be used with 3D subsetlibraries to operate high transducer density 2D antennas in 2D modes.The present invention can use its antenna structure for housing utilityelectronics and microwave remote reporting gear and also have it serveas a radio or TV transmitting antenna.

Given a chosen bandpass, the accuracy of the underlying mathematicalmodel is determined by the accuracy of the sampling, the level of systemelectronic noise, the level of environmental random noise, and signalprocessing accuracy, and how well data sampling criteria are met.Environmental considerations, the physical process, the anticipatedscenario, and operational constraints may dictate the choice of antennatransducer system to be used. Each embodiment should preferably employ aself consistent configuration, so that the system outputs reliableselected information to a reporter for decision making by a human orother external device.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The foregoing, as well as other objects of the present invention, willbe further apparent from the following detailed description of thepreferred embodiment of the invention, when taken together with theaccompanying drawings and the description which follows set forth thisinvention in its preferred embodiment. However, it is contemplated thatpersons generally familiar with mathematical wave propagation models andwith communications and direction finding systems and their theory willbe able to apply the novel characteristics of the structures illustratedand described herein in other contexts by modification of certaindetails. Accordingly, the drawings and description are not to be takenas restrictive on the scope of this invention, but are to be understoodas broad and general teachings.

Referring now to the drawings in detail, wherein like referencecharacters represent like elements or features throughout the variousviews, the high resolution, vectorized three dimensional multiple targettracking and signal reconstruction system of the present invention isillustrated in various embodiments.

The general structure of the physical components of the presentinvention is described below, as is the basis for the realization ofsignal vectors, stated with examples. Also described is the basis forconfiguring embodiments constructed in accordance with the presentinvention and procedures for obtaining selected information.

The overall structure of one preferred signal reconstruction anddirection finding system, generally 10, constructed in accordance withthe present invention is depicted in FIG. 1. Transducers 12 of antennas,such as acoustic antenna AC, electromagnetic antenna E, and/or seismicantenna S, convert physical wave fluctuations at the location of eachtransducer into electrical fluctuations. Mixer and signal conditioningunits, generally SCU, can amplify, filter, and mix the signals of eachtransducer as requirements dictate. The SCU outputs are then passed toanalog-to-digital converters, generally A/D, to digital filters,generally DF, operating consistent with temporal Nyquist samplingcriteria (Oppenheim and Schafer). Further signal processing takes placein an array processor AP (or computer CPU, possibly a parallelprocessor) on time series data output from the A/D converters, and/ordigital converters DF, and data reduction take place under software. Thearray processor AP feeds a reporter, generally RPTR, for transmission ofresults on selected information in suitable form to humans.

System 10 is illustrated having acoustic, seismic, and electromagneticcapability. It includes software for an optional calibration signal feedrunning from the computer processing unit AP through a calibratingsignal generator, generally CSG, to transducers 12. The software for thesignal calibration feed provides signals for calibration of the system10 and for verification of system performance within allowed tolerances.The above system in diagram 10 can also be used with an appropriatehydrodynamic sensor (not shown) for use in detecting hydrodynamicwavefields.

Although FIG. 1 only illustrates applications for acoustic,electrodynamic, and seismic wave types, possible solutions and wavetypes can include scalar, vector, and tensor fields associated withcoordinate systems appropriate for different possible antenna symmetriesand physical processes (acoustic, seismic, electromagnetic, andhydrodynamic) and environmental conditions. Each such model isassociated and consistent with implementation of the conceptual basisfor the embodiment as described in the above Summary as applied to thepertinent type(s) of physical wave propagation, or consistent with anincomplete implementation if the desired selected information allows.

The propagating physical wave and the detected or transducer sampledphysical wave may differ. For example, if the propagating wave iselectromagnetic, the transducer detected wave may be that of electriccharge and current densities on the surface of a conductor as induced bythe propagating wave. Mathematical models used in accordance with thepresent invention provide the map between sampled data and the chosenphysical wave fields to model.

The present invention includes procedures for obtaining signal vectors.Transducers can be considered as placed upon a surface, real orimaginary. The type of transducers utilized should be consistent withthe chosen mathematical model for the chosen physical wave field beingsampled. The transducers should preferably be small compared withrelevant wavelengths, so that measurements can be associated withspecific transducer locations on the transducer surface. If transducerspacing, number, and the temporal sampling rate for wave fieldfluctuations meet Nyquist sampling criteria for waves on that surface,then the mathematical representation for the wave fluctuations ispreferably uniquely determined over that surface for the period data iscollected. Furthermore, even if a choice is made for completemathematical model for the incoming wave field, and transducer type andsampling is consistent with this choice, a mathematical model for thefield can also be determined within the vicinity of that surface. Hence,a proper discrete set of samples can define a signal vector, and theFourier Transforms of these temporal sample sets can also define signalvectors.

Signal vectors can also be obtained as expansion coefficients of partialwave expansions (PWEs). The latter are defined by separable or nearlyseparable solutions to wave equations defining the mathematical modelsfor the relevant physical wave fields, those formed through the processof separation of variables. Each partial wave is labeled by theseparation constants defining it. For a properly configured system, thesignal vectors defined by expansion coefficients of suitably truncatedpartial wave expansions are equivalent to those described above, and canbe related by mathematical transformation. Integral forms for solutionsof wave fields, such as those developed by Sommerfeld and Weyl(Stratton) can also be used to define signal vectors.

The procedures allowing for the construction of a chosen mathematicalmodel for a physical wave field in the neighborhood a surface followfrom knowledge of the field and required spatial and temporalderivatives on the surface, and mathematically established uniquenesscriteria for the field's mathematical model tell what is required.Nyquist criteria tell when a sufficient number of samples at asufficient number of spatial locations are taken for a given bandpassand time period. Consequently, with sufficient temporal sampling ratesthe model for the chosen physical wave field everywhere on the surfacecan be constructed, and the field on that surface can be numericallydifferentiated, so that temporal Fourier transforms in time are alsoknown thereon in principle. For certain choices physical wave fields andmathematical models and types of transducers, implied knowledge ofspatial and temporal derivatives along the surface allows constructionof the wave field model in the neighborhood of the surface, when thelatter is needed as selected information. The dispersion relation givingwave number as a function of frequency is known from the wave equation,so the maximum number of wavelengths present along the surface can bedetermined for each frequency (considering various possible directionsfor incoming waves). This determines required antenna transducer spacingaccording to the sample criteria and the angular resolving power aswell, which is given by the angular aperture of the shortest possiblewavelength along the surface, a result consistent with Lord Rayleigh'scriteria for “just” resolution in optics (Jenkins and White).

Signal vectors can be the ordered set of samples (time series data)collected from the transducers via A/D conversion over some temporalwindow. Signal vectors also can be the set of Fourier coefficientsobtained discrete Fourier transforms of this time series data. Or, theycan be the expansion coefficients of a suitably truncated partial waveexpansion (associated with a coordinate system for which the waveequation is separable). Other signal vectors can also be obtained, forexample, from a discretization of integral solutions to a wave equation.For all such cases, the set of signal vector components will besymbolically represented by {s_(α)} and the signal vector by s, where αis a collective index.

The signal vector index a differentiating components of the signalvector may characterize the set {jt_(k)} of the original samples (jlabels the transducer where the sample at time t_(k) was taken), assuch, it characterizes the original sample set time series. It may alsocharacterize the frequencies and transducer label of the Fouriertransformed time series data. In the case of partial wave expansion, itcharacterizes the indices labeling the distinct partial waves, such asthe traditional (k,l,m) of the expansion for spherical partial waves,etc. The particular choice of signal vector representation depends uponthe selected information being sought and the nature of the environmentin which the system is to be used. For example, for sources at longrange, the plane wave PWEs provide a useful signal vector representationfor spectral components of incoming signals, while spherical wave PWEsare useful for descriptions of same in spherical polar coordinates whenoutput for bearing and elevation angles of sources is desired.

For a carefully configured embodiment the different signal vectorrepresentations are equivalent, a situation occurring when embodimentresolving power, temporal and spatial sampling, and hardware processingare consistent. The Fast Fourier Transform (FFT) relates the spectraldomain signal vector to that of the temporal domain. The partial wavefunctions evaluated at transducer locations define the transformationfrom one of the former to one of the partial wave representations of asignal vector. In fact the spectral domain signal vector is that of apartial wave expansion in harmonic functions. The aforementionedrepresentations of signal vectors are of course equivalent to somespecifiable accuracy, for example, the accuracy with which thetruncations of the infinite PWEs are valid, or that to which a low passfilter is effective in meeting Nyquist sampling criteria.

The mathematical description of a physical wave field may be amulti-component entity, as with seismic and electromagnetic waves. Inthe latter case, the signal vectors may be obtained through electric andcurrent vector densities on a metallic surface. The Kirchoff typerepresentations and associated uniqueness theorems for each choice offield for which an embodiment is to be constructed provides a guide towhat data need be sampled. The same information can be obtained throughconsideration of what is required to create a power series expansion forthe mathematical model using the wave equation. Use of the wave equationand proper temporal and spatial application of the sample theoremprovide the latter. For a complete specification of a mathematicalmodel, depending on desired selected data, more than one type oftransducer may be required (for example, through use of both velocityand pressure sampled microphones in acoustics, capacitors and/orinductors in electromagnetics). Seismic and hydrodynamic waves treatablewith linear mathematical models exhibit analogous properties.

The choice for a signal vector representation should preferably be madeon the basis of numerical efficiency in obtaining the selectedinformation and upon the dictates of the appropriate uniquenesstheorems. The most efficient are typically those for which thecoordinate system reflects the symmetry of the antenna system andenvironment and for which the wave equation allows for the separation ofvariables. Example antennae of such “efficient” systems are illustratedin FIGS. 2-6.

If the antenna presence significantly disturbs the propagation of thephysical wave, then the model solution to the wave equation for waves ofeach incoming direction should preferably include the scattered wave aswell. The signal vector should preferably as much as possiblecharacterize the total wave field of both the incoming and scatteredwave, as required by the selected information sought, for accurateresults.

The antenna is the physical device containing transducers through whichthe fluctuations of the physical wave or induced “charge densities” areconverted into electrical fluctuations. The specific form of theconversion process is assumed to be understood and linear, so that thesuperposition principle applying to composite waves of multiple sourcescan be tracked in the electrical fluctuations. Transducers define a mapbetween physical wave field fluctuations Ψ and voltage or currentfluctuations σ.

After amplification, A/D conversion, signal conditioning, and digitalbandpass filtering, any decimation, and possible Fourier transform (viaFFTs) of properly windowed time series from each transducer channel,various representations of the signal vector are obtained from linearequations of the form:

${\sigma_{A} = {{\sum\limits_{\alpha}{s_{\alpha}K_{A}^{\alpha}\mspace{31mu} j}} = 1}},\ldots\mspace{14mu},{N_{s}.}$In this signal vector equation, σ_(A) may be proportional to the A^(th)component of the wave field, as might be in the acoustic applicationwith use of microphones, or to surface charge or current densitycomponents, as in the electromagnetic case (related to the normalcomponents of the electric field and the tangential components of themagnetic field at a conducting surface, respectively). The coefficientmatrix elements K^(α) _(A) may coincide with the identity matrix if thesignal vector represents the samples themselves, or may be the partialwave functions evaluated at transducer locations in the case of PWErepresentations of the signal vector.

Antennae with microphone transducers may be used for sensing pressurefluctuations (FIGS. 2A, 2B, and 6), with capacitive transducers forsensing surface charge densities (FIGS. 3A, 3B, 5A, and 5B), and withinductive transducers for sensing surface current densities (FIGS. 4A,4B, 4C, 5A, and 5B). For the acoustic case, depending on the level ofmathematical model the signal vector should define, the transducersmight include both pressure and velocity type microphones. In theelectromagnetic case, antennas may combine capacitive and inductivesampling using capacitive transducers 54 and inductive transducers 56.In the latter case when the two types of transducers 54, 56 are takentogether, sampling would allow the polarization of incoming waves to beaddressed as selected information and also allow field reconstructiongiven proper scattering models for the antenna structure. For thecapacitive electromagnetic antenna of FIG. 3A, only the surface chargedensity sampled by transducers 34 of FIG. 3B, related to the normalcomponent of the electric field at the surface, is required fordetermination of the directions of incoming waves, as an analysis ofelectromagnetic vector partial wave solutions can show. However, ifsignal reconstruction and or polarization information is required,additional sampling may be needed, as with using the inductivetransducers of 56 of FIG. 5D, or a combination of one inductivetransducer 56 and one capacitive transducer 54 set therein. Note thatany of the antenna shapes may be used for acoustic or electromagneticsampling in FIGS. 3A, 4A and 4B, and in FIGS. 5A and 5B and FIG. 6.

Other possible transducer types not specifically illustrated in theFigures above include hydrophones (sampling acoustic pressurefluctuations in fluids), geophones (sampling displacement velocities inseismic media), total field magnetometers (sampling magneticfluctuations parallel to the earth's magnetic field), vectormagnetometers (sampling fluctuations in the magnetic field components),and thermistors (embodiments sampling temperature fluctuations ofoceanic internal waves). Magnetometers can also indirectly samplemagnetic fluctuations in oceanic tidal, internal, tsunamic, and surfacewaves. The present invention is not limited to these types, it can beused with any transducer set sampling entities associated with wavesmathematically modeled by linear equations. The transducers shouldpreferably, however, be relatively small in comparison to the shortestwavelength envisioned in the process, so that samples may be associatedwith points on the closed transducer surfaces. Antennas with opensurfaces may also be closed using suitable spatial windowing techniquesanalogous to those used in temporal sampling.

Depending upon whether the dimensionality of the signal vector coincideswith the number of transducers utilized (generating utilized datachains) there exists a number of numerical methods that can be utilizedfor the inversion of the signal vector equation (Math works). FastFourier transforms, and matrix inversion and least square techniqueshave been employed in embodiments to invert the truncated partial waveexpansions of different coordinate systems and physical waves. However,if the inversion process is not one-to-one, then there can be ambiguityin any subsequent signal reconstruction, with a potential for subsequentloss of information.

The system configuration sets the resolving power, the size of theantenna, the number of required transducers, and the dimensionality ofthe signal vector. A minimal configuration provides for the minimumnumber of transducers allowing for the definition of a signal vector(the number of its effective independent components thereof), asrequired by the Nyquist criteria, and as discussed above this alsoestablishes the resolving power. The latter, according to Rayleigh'scriteria for “just resolved” follows when the maxima of a surface waveof one source is at the first null of that of another, a criteriadeveloped for consideration in optics when two sources are present. Thecriteria coincides with the minimal condition set by the Nyquistsampling criteria, that there must be at least one transducer for eachhalf wavelength along the surface. Here, we define the embodiment'sresolving power, generally RP, is defined as the minimum number ofresolvable sources on any closed circle centered on the antenna.

Assuming that any incoming direction is possible, the maximum projectionof the wavevector k corresponds to the shortest wavelength at any pointon the surface. Then, according to Rayleigh's criteria for “justresolved”, the resolving power is: RP=2kR. But, this is just twice thenumber of wavelengths around the imaginary circle. Accordingly, theNyquist criteria also establishes Ns=2kR as the minimum number ofrequired transducers to be uniformly aligned on such a circle, or thenumber needed per unit length if the transducer surface is not made ofcircles. Ns also coincides with the utilized dimensionality of thesignal vector required for the highest frequency considered for a givendirection, also according to the sample theorem. For a sphericalsurface, the number of required transducers and signal vectordimensionality is then (2kR)² if the resolving power is independent ofloop orientation. If not every incoming direction is possible, theuniformity requirement for resolving power can be relaxed.

The considerations on resolving power and number of required sensorsrefer to the σ_(A) of the signal vector equation for a scalar field. Forvector and tensor fields, the result may differ. For electromagneticwaves, if the embodiment is needed to carry out a complete signalreconstruction, the number of required sensors is twice that above, asthere are two polarizations. The result is then that of a sum over thetwo polarizations, which would be the same as that for a scalar field.Note that for propagating electromagnetic waves not all three of thecomponents of the electric and magnetic fields are independent.

Data reduction consists of determining the selected information desired.It involves detection, direction finding, source classification throughspectral decomposition, and signal reconstruction. It makes use of thesuperposition principle, pre-constructed libraries of mathematicalmodels of possible sources, and certain geometrical entities. The latterinclude scalar products, signal surfaces, energy surfaces, detectionsurfaces, and adaptive directional maps.

The superposition principle regards the signal vectors s of receivedcomposite signals as the sum of those of possible sources s_(q) andnoise. This applies to any form of the signal vector, whether in thesample, frequency, partial wave, or integral form domains.

The most fundamental signal vector library is the directional library(DL), which is created and developed from signal vectors of possibledirections and frequencies within the bandpass of interest. Let s_(k)denote such a library element, the wavevector k corresponding to theincoming wave spherical polar angle direction (θ_(k), φ_(k)). Such alibrary can form the set of signal vectors of point sources at very longrange, so that the modeled incoming waves are plane when they pass overthe embodiment's antenna. The directional library can be constructedusing analytical input (as obtained from the partial wave expansion ofplane waves) and/or numerical models.

A signal surface is the surface defined by scalar productss(θ_(k),φ_(k))=(s,s_(k)) between the signal vector of the sampled waveand library elements with the incoming signal vector for all wavedirections k. The “radial” coordinate for each point on the surfacecorresponding to a DL element is the value of the scalar productcorresponding to that direction of k. The metric for this scalar productis that which is appropriate for the signal vector representation. Forthe sample and frequency domains representations, the metric isdiagonal, and each such diagonal element has unit value.

To each signal surface there corresponds an “energy surface” denoted bys²=|s(θ_(k),φ_(k))|². Note that each library element can have its own“signal surface”, defined by scalar products of the form (s_(k),s_(k′))for all possible wavevector directions k′. Each such element alsotherefore has its own “energy surface” s_(k) ²

The “adaptive signal surface” is obtained by weighting the value of thesignal surface for the direction of k by the inverse of the average ofthe noise background signal energy surface for the same direction, theaverage being taken over a number of temporal windows or realizations.

The adaptive signal surface is a distorted signal surface so that thedirection associated with maxima in the signal surface's energy surfacemay not define the correct direction to a source. The “noise adaptivesignal surface” reduces the contributions of noise sources to the signalsurface for directions for which the average noise background is largerelative to other directions. Such noise sources may include knownsources whose presence is also known and understood but not of interest.Thus, the adaptive signal surface procedure is particularly useful forreducing the effect of background interference from known sources not oftracking interest. In such instances where distortion exists, anadaptive map should preferably be used to obtain the true directions forvectors associated with sources. This map will be defined below.

There are two classes of detection criteria. One is energy detection,appropriate for the situation when only a single source of interest isknown to be present, or the source is already known to be well resolved,and the signal-to-noise ratio is good. The second is that of directionaldetection, useful when the presence of multiple sources are suspected oranticipated, the sources may not be all resolved, and/or when the signalto noise ratio is low.

There are also different levels to be reached in declaring a detection.The first is that of a probable detection. A probable direction ispreferably automatically assigned to every detection. The notions forprobable detection and probable direction apply regardless of whetherthe signal surface utilized is adaptive or not.

Energy detection is a threshold detection based upon the energy surfaces²(θ,φ;ω). If the maximum value for the latter as a function of (θ,φ)exceeds that of the averaged noise background “energy” by somepreassigned number, then a probable detection is declared. Thepreassigned number can be based upon a false alarm rate following from amodel for expected detections from some noise model.

Directional detection utilizes signal and library direction vector raydirection properties. With directional detection, signal vectors(including directional library vectors) are normalized such that theirsignal surfaces have value unity for the direction for which thecorresponding energy surface has a maximum value. A probable detectionis declared if the absolute value of the difference surface resultingfrom the difference between the signal surface of the incoming wavefield and that of a directional vector integrated over all directions topoints on the difference surface is below some threshold. Thus, thedetection is based upon a model for the shape of the signal vector of agiven source, instead of upon the signal level relative to somebackground and threshold.

For energy detection, the directions of the probable sources are thosefor which the signal energy surface has maximum values exceeding thethreshold. For directional detection, the assigned probable direction isthat for which the total “energy” of the difference surfacecorresponding to a particular direction vector has its minimum value.Probable directions associated with the adaptive signal surface arepreferably assigned only after the adaptive map is employed.

The adaptive map transfers the directions assigned to sources of signalsurfaces constructed using the adaptive scalar product to truedirections. The directional criteria can result in the signal surfaceand adaptive signal surface assigning different directions to the sameincoming signal detected if the time averaged noise background “energysurface” is not isotropic. The map can be computed off line by notingthe adaptive signal surface directions assigned to the modeled incomingplane wavevector directions used to define the directional libraryvectors using the two metrics, and constructing a table lookup for thiscorrespondence.

For “energy detection,” the direction assigned to the probable detectedsource is that of the maximum of the signal surface, the value of (θ,φ)belonging to the vector k of the s_(k) defining the signal surfacemaxima. This assignment can be made to other maxima provided those areat least just resolved, according to the criteria discussed above.

For directional detection, the assigned direction is that belonging tothe s_(k) producing a minimum value for the signal vectors satisfyingthe criteria for probable directional detections, provided the minimumis at least just resolved from other minima.

If multiple sources are encountered, it is preferable to ascertainwhether they are resolved, and if so, incorporate the resolvingcapability into the detection criteria. A local resolving power as afunction of direction is ordinarily readily determined.

The local resolving power is found by observing the functionaldependence of the scalar product (s_(k),s_(k′)′) and determining theangular separation γ_(RP) between the directions for which this scalarproduct has its maximum value and its first minimum away from thiscentral maxima. The local resolving power is then defined by: LRP=2π/γ_(RP), where γ_(RP) is the angle just described, hereafterreferred to as the resolving angle. Conceptually, LRP is typically anestimate of the number of equally spaced sources that could be resolvedalong a circle. For a two dimensional transducer surface, the localresolving power can be defined as the geometric mean of the localresolving powers for two orthogonal directions.

The detection rate surface is the surface defined by the rate at whichdetections occur per unit solid angle, as defined by probabledirections, the rate determined over a number of data collectionwindows. Noise interference effects generate detections even whensources of interest may not be present. The detection surface forbackground noise alone is denoted by DR_(N), and in the presence ofsignals of interest, by DR_(S+N). The detection rate surfaces ofprobable detections can be defined after a sufficient number ofrealizations has taken place to yield a sufficiently smooth function ofthe spherical and polar angles.

Detection measure surfaces provide for the declaration of a detectedsource. One such measure could be the surface defined by the noiseaveraged detection ratio (DR_(S+N)−DR_(N))/(DR_(S+N)+DR_(N)). Thisdefinition requires that a number of realizations be employed to computethe average, and that the ratio be considered a function of angle.

Declaration of a detected source is made if the measure function ofdirection has maxima exceeding a detection threshold (DT); if the shapeof the maxima is judged consistent with noise properties; and if theangular distance between such maxima is consistent with the embodiment'sresolving power. Thus, the concept of resolving power plays a role inthe declaration of multiple source detections.

In some instances, such as when the “energy” (in the sense discussedabove) is sufficient and only one source is known to be present, adetected physical source can be declared directly. The detectionmeasure-based procedure can potentially permit detection at thebackground level less the antenna array gain, even when multiple sourcesare present.

Signal averaged detection follows from a different process. It isparticularly applicable to impulse signals such as those of projectileshock and blast waves, and in estimating the directions of continuoussignals with identifiable spectra, such as those associated withharmonic chains of piston engines.

For impulse waves belonging to short duration single occurrences, thedetection rate surfaces and temporal averaging processes described abovemay not be particularly useful. But such impulse signals are broadbandin nature, and the signal surfaces can be averaged over frequency. Thenoise fluctuations of the different frequencies have different signalsurface oscillation wavelengths, which average out in the summationprocess, while the surface functions at their maxima are normalized tounity and add coherently within the resolving angle. In this type ofaverage, the normalized signal surfaces (normalized by their maxima asdescribed above) are summed and divided by the total number of spectralcomponents involved. Either the energy detection or directionaldetection (appropriately modified) process can be applied to the result,the averaging process also can be limited to frequencies having probabledetections. This technique has been found to yield excellent results indetecting gunfire and shooter directions, as well as those shock wavesassociated with the projectile. It will also be useful in the trackingof turbine engines, which also have broad band spectra. The detectionrate surface process could also be applied to the spectrally averagedsignal surface if the events are repetitive.

In the case of piston engine harmonics, the signal averaging summationis carried out only for elements of the harmonic chain. This is a usefultechnique since the Doppler shift of elements of the harmonic chainyields another harmonic chain (with different spacing for chainelements) and direction finding, and detection of individual elements ofthe chain may not yield accurate results if the signal levels are toolow. Again, the signal surfaces involved must be normalized to unity inthe direction they have their maxima.

For sources at very long range, or for where they are at rest, or whentheir directions are changing little with time, the properly normalizedsignal surfaces could be averaged over data collection temporal windows.Also, an average over both temporal windows and frequency could be made,depending upon the anticipated nature of the sources and theenvironment. Again, detection rate surfaces based detection criteria areapplicable.

If the noise based adaptive signal surface is used in signal averageddetection, it should preferably first be mapped into a standard signalsurface using the adaptive map for each frequency before signalaveraging takes place, if the noise background changes with time. Thisis because the signal surfaces of different frequencies may havediffering distortions.

The choice of which signal detection process is used depends upon theanticipated signal to noise ratio, whether or not the signal has broadspectral content or a harmonic chain, and the duration of the signal.The signal surface averaging processes are particularly useful becausethe effects of random sources and fluctuations generated by randomprocesses affecting paths tend to average to zero, in sharp contrastwith averages involving “energy” type functions. Source directions comewith the detection processes.

For noise averaged detection, the assigned direction are the maxima ofthe detection rate measure surface meeting the detection measurethreshold, provided the maxima is at least just resolved from othermaxima as per the discussion on noise averaged detection above.

For signal averaged detection, the direction assigned is that of themaxima of the signal averaged signal surface exceeding some threshold,as with directional detection. There can be more than one such directionif there is more than one maxima exceeding the detection threshold,provided the maxima involved are just resolved.

For noise averaged signal averaged detection, the assigned direction isthat of the maxima in the measure surface. There can be more than onesuch assigned direction if there are other maxima meeting the detectionthreshold criteria, provided those maxima are at least just resolved.

Source spectral content is established once the s_(q) have beendetermined for a resolved source. Given the s_(q) weighted of theircontributions as defined by the scalar products defining signalsurfaces, the s_(q) can be transformed to the frequency domain. Thefrequency domain s_(q) coincides with the Fourier coefficients of theincoming time series data of the q^(th) source, and its spectra isdefined. This amounts to executing the signal vector equation with theσ_(A) as the result and the weighted s_(q) as input. The resulting|σ_(A)|² then provides the power spectra. The source level of aparticular source q can be estimated from a propagation model for thegiven environment, taking into account attenuation and geometricalspreading.

Signal reconstruction and signal information content are carried out bytransforming from the derived representation for the weighted frequencydomain s_(q) and then using the inverse Fourier transform (discrete) togo to the equivalent sample representation of the s_(q), This must becarried out for a series of overlapping temporal data collectionwindows, where in the set of field values τ indexes the sample set orsample window of the j^(th) transducer at the listed coordinates foreach time t_(k) of the window. If this is done for a series ofoverlapping temporal windows, windowing functions W(t_(k)−τ) can beemployed to construct from these sets a smooth time series over anextended time period. This process permits determination of informationcontent or reconstruction of received signals using digital signalgenerators carrying out digital to analog conversion, provided theembodiment bandwidth is sufficient for the resolved signal and allsignificant spectral components of the resolved signal are included.

If the proper set of transducers are employed in conjunction with thewave equation or surface integral expressions of the Khirkoff type, asper associated uniqueness theorem criteria, a mathematicalrepresentation of the field in the neighborhood (or vicinity) of theantenna can be carried out. In this case selected, information can beobtained after the mathematical model of the wave field has beenconstructed from obtained signal vectors. This can be done using thewell known Neother's theorem techniques applied to mathematical modelLagrangians to obtain energy and momentum vector densities (Roman)explicitly carrying directional and frequency content.

Note that it is not necessary to temporally sample at twice the highesttransmitted frequency to get desired modulation information as selectedinformation. The processed signal need only be heterodyned and sampledat a rate of at least twice the highest modulation frequency, since thesignal vector equation can be scaled so that all the transducer signalsare sampled relative to one.

Several example embodiments and deployments are illustrated in FIGS.2-14, but it is to be understood, however, that the present invention isnot limited to the examples and embodiments herein disclosed.

For each antenna illustrated, transducer spacing depends upon thedesired resolving power, which should be compatible with the number oftransducers allowed. The resolving power need not be the same for alldirections.

For a spherical antenna having spherically symmetric resolving power,the Nyquist criteria requires N_(s)=(2kR)²=(LRP)². The partial wavesdefining signal vector components can be the spherical harmonic-basedset of consisting of the j_(l)(kR)Y_(lm)(σ,φ), where j_(l) denotes theBessel function, Y_(lm) the spherical harmonics, k is the wavenumber,and R is the spherical radius. The signal vector index α consists of theindices k, l, and m for each frequency. The series is truncated for amaximum value l_(max)=(LRP−1). The Fourier and spherical harmonicrepresentations for the signal vector are equivalent. Near equal angularspacing of transducer elements can be achieved by having element planeswith near equal polar angle spacing containing groupings of (2l+1)transducers, equally spaced within.

The spherical antenna, generally 22, of FIG. 2A is of the type which isappropriate for acoustic microphone transducers obeying these placementrules. The insert in FIGS. 2A and 2B indicates generally how theelectronics, such as SCU, A/D, DF, AP, and RPTR, can be mounted withinthe mast. With thin structural elements and transducer dimensionsrelative to a wavelength, it has not yet been found necessary to includethe influence of the element scattered waves on the transducers. Othercoplanar grouping of transducers could involve √{square root over(N_(s))} equally spaced transducers in √{square root over (N_(s))}planes, with equal polar angle spacing, but the result does not givenear uniform resolving power for all directions.

For the cylindrical antenna 30 of FIG. 2B, the partial waves consist ofproducts of ordinary Bessel functions of the radial coordinate, theexponential function along the axis, and harmonic functions for thebearing coordinate, if a cylindrical partial wave representation is usedto define a signal vector. This antenna would require windowing in theaxial coordinate in order to simulate the condition that a closedsurface contains the transducers, since practical systems cannot beinfinite in length. A maximum spacing of λ/(2 sin φ) between transducersis preferably required along the cylinder's axis, where λ is thewavelength at the highest frequency and φ is the highest anticipatedangle of elevation over the plane of a ring. For a bearing resolvingpower of L RP=2ka, the number of microphones along equally spaced ringsshould be equal to or larger than 2ka, where k is the wave number of thehighest frequency to be studied and a is the cylindrical radius, andconsistent with the above, 2ka such rings 26 should be used at aminimum. Note that the first and last ring need not be at the “ends” ofthe cylinder where the windowing function vanishes. With this type ofconfiguration, generally there is an equivalence between the Fourier andcylindrical partial wave representations of the signal vector.

FIG. 3A illustrates a spherical electromagnetic antenna, generally 32,with capacitors, generally 34, whose construction is illustrated in FIG.3B, having an insulator 38 and another plate 39. Capacitors 34 can haveone capacitive transducer plate being the surface 36 of the highlyconducting metallic spherical shell. The same transducer placementconsiderations apply as discussed for FIG. 2A. The capacitor's impedanceover the bandpass should be consistent with electronics and samplingrequirements on time constants, and the capacitors should preferably besmall in comparison to a wavelength. At cell phone frequencies, suchantennas are capable of high density transducer placement and resolvingpower and portable for placement with individuals or on vehicles.

FIG. 4A is an electromagnetic cylindrical ring antenna 40, theelectromagnetic counterpart of the antenna of FIG. 2B. The transducersare inductors 42 as illustrated in FIG. 4C and are equally spaced onrings 44 (FIG. 4B). The inductors 42 are insulated windings over thehighly metallic ring surface 46, as illustrated in FIG. 4C. Inductoraxial and angular placement is the same as the transducer placement asper the discussion on FIG. 2B. The inductors should preferably also besmall in comparison with utilized wavelengths and their electronicimpedance should be consistent with electronic impedance requirementsover the bandpass. At cell phone and other high frequencies, suchantennae can have high density, high resolution, and be mounted as“whip” antennas above vehicles.

Use of high density antennae also permits adaptive reduction of vehiclenoise using the adaptive noise metric, as discussed above, or noisereduction using Gram-Schmidt orthogonalization applied to the signalvectors. Such antenna when mounted as tall structures could potentiallysupport highly accurate systems for measuring elevation angle as well asthe bearings of low elevation angle incident radiation. Note that thistype of structure, with microphones or hydrophones replacing inductors42, also can be used as acoustic systems in air and water. In the lattercase, when embedded in the ground with hydrophones, as in a well, theycan be used to map noises in underground facilities, when propermodeling and boundary conditions are employed. If the overall antennaedimensions of FIGS. 4A and 4B are small compared to utilizedwavelengths, antenna scattering need not be accounted for in acoustics,but must be accounted for in the electromagnetic case when metallicsurfaces are utilized. Some scattering models exist in the literaturereference above.

FIGS. 5A and 5B depict an ellipsoidal, or prolate spheroidal, antenna,generally 50, and a cylindrical shell antenna 52, respectively,associated with separable coordinate systems and also capable ofsupporting PWE based signal vectors. They can be used with hydrophonesfor water applications, with microphones for acoustic applications inair, with capacitive transducers 54 as in FIG. 5C, or with inductivetransducers 56, as shown in FIG. 5D. In the case of inductors, with two“polarizations” for the inductive transducers as 55 in FIG. 5C, such anantenna can determine the polarization of incoming waves and be used forelectromagnetic signal reconstruction, as discussed above.

With the antennae 50, 52, and the spherical shell antenna 32 of FIG. 3A,the modeling library signal vectors should include shell scatteringeffects for both electromagnetic and acoustic waves. If desired, theelectromagnetic transducers could be replaced with acoustic microphones.

A theoretical analysis shows that the signal vectors of incomingelectromagnetic waves at long range are characterized by the expansioncoefficients of vector spherical harmonics, so that capacitivetransducers suffice if the desired selected information is confined totracking information. The sampled charge and current densities are thoseof signals including the possible polarizations. If the selectedinformation also requires wave polarization information or individualsignal source reconstruction, then preferably, the complete set oftransducers 54, 56 depicted in the FIGS. 5C and 5D can be employed. Thespherical antenna would use spherical Bessel functions and vectorharmonics for its vector partial wave expansion, while the ellipsoidalantenna 50 could use “corresponding” prolate spherical coordinates andfunctions. If the minor axis of the ellipse is chosen to be the onerotated about, then the oblate spheroidal coordinates and thecorresponding PWE would be used. The complete number of requiredtransducers 54, 56 is double the number required in the acoustic casefor the spherical antenna of FIG. 2A for the same wavelength, aconsequence of the two polarizations. In any case, transducer spacingshould preferably be determined by the maximum projection of thewavevector for the highest frequency onto the surface containing thetransducers 54, and the spacing should preferably be less than or equalto half the length of the shortest corresponding projected wavelength.

Supporting electronics can be built into the antenna masts and/orspheres and/or ellipsoids as desired. Such antennas are very practicalfor electromagnetic frequencies running from short wave and VHF to cellphone frequencies. The spheroidal antenna 50 would use vector wavesolutions as well, but would employ cylindrical vector harmonics as inStratton (referenced above), the vector harmonics and the vector wavesolutions involving derivatives of the aforementioned functions.

With the capacitive antenna, the transducers 54 and 34 sample surfacecharge densities on the surface, while with the inductive antennasurface, surface current densities are sampled. Complete scatteringsolutions for incident plane waves with the proper polarizations canyield the necessary connection between incoming fields of sources atlong range and induced surface charge and current densities. Theconnection is defined by well know boundary conditions relating thesurface charge and current densities to the normal components of theelectric field and the tangential components of the magnetic field. Forthe electromagnetic antennas mounted on the metallic surfaces, thecapacitive and inductive transducers should also have dimensions andstructure compatible with the impedances required by the electronics andsampling criteria, i.e., time constants associated with the sampling.

FIG. 6 illustrates an antenna 60 suitable for treating coupled incidentand earth surface reflected acoustic waves in regions where the earthand/or mounted surface is flat on a scale large in comparison to awavelength. Again, use of thin structural elements 62 can make itunnecessary to determine the waves scattered by the antenna. Thecoupling of the incident and surface scattered waves introducesrelationships between components of the signal vector, reducing thedimensionality of the processing space and decreasing computationaldemand.

FIG. 7 illustrates an application of the present invention, whereinwhere small high density antennae, generally 70, can be deployed on avehicle 72. Shock, blast, and electromagnetic waves typically have shortwavelengths in comparison to vehicle dimensions, and higher frequenciescan be utilized. For a given natural local resolving power LRP, theantenna size can be reduced. A traceback program tracking back along raypropagation paths can be used to locate resolved sources of gunfire 74and shock waves, provided that contour map data is also supplied for theenvironment. Selected information can also be obtained for cell phones76 using electromagnetic antenna 78.

FIG. 8 illustrates deployments of the present invention where highdensity, high resolution antennae, generally 80, can be used with signalprocessing to help null out certain noise, such as noise from a vehicle82, as in removing vehicle-generated noise coming from the vehicle 82itself. Use of the noise metric and the associated mapping techniquewould allow tracking of sources of interest, particularly shock andblast waves, at wavelengths which are short in comparison with vehiclesize, even with significant vehicle noise. Small spherical andcylindrical high density arrays can be useful on relatively noisyvehicles. Traceback programs can also be employed for the location ofsources of projectile 84 firings, given contour map or triangulationdata. For lower acoustic frequencies, microphones and electromagnetictransducers can be placed along the body of the vehicle. In this casethe boundary conditions associated with scattering off the vehiclesurface should preferably be accounted for in the wave propagation modelused to construct the directional libraries, as is done with theelectromagnetic antennas shown in FIGS. 3A through 5B. The noise metricand associated adaptive mapping techniques can be employed to obtaintrue directions.

Other useful antenna system deployments can be made in accordance withthe present invention and can include severe storm 90 tracking withbuilding-mounted spherical acoustic and electromagnetic antennas,collectively generally 92, as depicted in FIG. 9. Combined acoustic andelectromagnetic systems can provide range data for near simultaneouslyresolved thunder and lightning 94 bursts, while visitors can be trackedand monitored with acoustic arrays and traceback programs.

FIG. 10A depicts a towed, or, surface-suspended antenna array 100, andFIG. 10B depicts a bottom-mounted antenna array 102, with both beingconstructed in accordance with the present invention. Such a system canemploy hydrophones, thermistors, or magnetometers for detecting shipengines, internal waves of swimmer delivery vehicles, tsunamis, shippingtraffic, etc., depending upon antenna and wave scales. The towed antenna100 for side acoustic scan sonar applications of the types illustratedin FIGS. 5A and 5B, with electromagnetic transducers therein having beenreplaced by acoustic transducers, is illustrated in FIG. 10B. Such sidescan operations, using active pulses 104, can provide 3D views ofsubmerged objects, such as mine 106 on the bottom or a tethered mine108.

A spherically symmetric and/or “tree” antenna 110 based system,constructed in accordance with the present invention, for a harborsecurity monitoring is depicted in FIG. 11A, along with a cylindricalmonitoring array 112 as shown in FIG. 11B. The cylindrical antenna 112may serve as an acoustic or hydrodynamic wave antenna (surface,internal, etc.), and could monitor for self-propelled and/or swimmervehicles 114 as well.

Mountain deployment of an acoustic spherical antenna 120 is depicted inFIG. 12, and such a deployment could be useful for remote traffic 122monitoring for situations where the terrain is not planar in theneighborhood of the antenna and where the antenna need not be mountedwith a particular orientation relative to the earth's surface. Atraceback program tracking back propagation paths can be used to locatesources of signals, such as from a sniper 124, emanating from themountain sides and/or other structures.

The wavelengths of interest and the nature of the propagating mediumplace restrictions on seismic wave antenna systems. Attenuation in theearth for interior waves is higher at higher frequencies, so lowfrequencies are generally more productive when making application towaves propagating through the earth. Embodiments such as those depictedin FIG. 13 might be employed in seismic exploration and/or facilitymonitoring. They can involve antennas, generally 130, with elementsburrowed into the earth's surface 134 with waves being generated usingan active mode, such as a bomb 136, as in FIG. 13, or planar antennas140, 142, as depicted in FIG. 14, for the detection of seismic surfacewaves, as detected by antenna 142, and for acoustic waves, as detectedby antenna 140. Geophones and/or magnetometers (not shown) can be usedas transducers for measuring fluctuations in seismic media or magneticinduced charges by metallic vehicles, respectively.

In simple seismic models, the wave equation modeling the physical wavecan be characterized by elastic moduli, and the waves are then bestdescribed by the P and S wave Hemholts decomposition (Lay and Wallace).In this case, both longitudinal and vector harmonics are needed. Use ofsmall bore holes 138 relative to wave dimensions of interest permitsignoring scattering by the illustrated seismic antenna structure, sothat, in one embodiment, only scattering of waves at the earth's surfaceshould preferably then be accounted for. A spherical antenna with anactive explosive source 136 would permit mapping of tunnel structuresand underground facilities, and multiple antennae would permit passivemonitoring and mapping of the facility.

FIG. 14 illustrates a combined acoustic, generally 140, and a seismicantenna array, generally 142, constructed in accordance with the presentinvention for measuring waves propagating 1 (in the neighborhood of thearray) along the earth's surface.

The antennae described above (with the exception of that of FIG. 13) cantypically be readily constructed and can provide for a minimal number offloating point operation, since the constant value of one of thecoordinates of the coordinate system describes each transducer surface.Other antennae are possible, though, and could use a random placement oftransducers, as might be done if the antenna must be placed remotely,such as, for example, in the scenario illustrated in FIG. 13 ifproviding small bore holes were not possible. If transducers arerandomly placed (such as by air drop, use of projectiles, missiles, orthe like), software, and knowledge of their random positions through usof the global positioning system (GPS), could potentially allow a subsetof the transducers to be sampled via radio link, or some othercommunications method, for the purpose of defining signal vectors. Asubset of the transducers consistent with the Nyquist sampling criteriacould then be selected. In such an embodiment of the present invention,the thus formed randomly-shaped, or near arbitrarily-shaped, antennaecould also be used, but there would likely be a higher demand for signalprocessing power for certain types of selected information, such as withlocal wave field reconstruction. Calibration of such antennae could bedone in various ways, and could include the detonation of one or moreexplosive devices at a predetermined location(s) within the vicinity ofthe transducers and reviewing the outputs of the respective transducersin response thereto.

Note that with configurations of antenna constructed in accordance withthe present invention and meeting minimal Nyquist sampling requirements,such antennas can also be used in the sample and frequency domainswithout reference to partial wave expansions, particularly if onlydetection and tracking information is required.

The present invention also includes a self calibrating system, generally150, shown in FIG. 15, which may include the self-calibrating systemcontained in FIG. 1. Calibration of the system 150 corrects fordeviations from desired component tolerances and verifies that thesystem is operating within prescribed tolerances. The linear nature ofthe processing provides employment of simple techniques. Signal outputfrom D/A converters (not shown) driven by time series from an arrayprocessing unit AP drives a calibrating signal generator CSG inputting acommon signal to transducer elements. The complex amplification for eachchannel, generally A, for this signal can be determined, and deviationsfrom a standard (which can be one of the antenna transducers or areference signal) can be used as a basis for numerical correction ofinputs. This insures that the system channels effectively are identicalon each frequency over the bandpass. This procedure can be also be usedto check that voltage outputs, generally V, (and/or current) of eachchannel are within system tolerances. The process can be carried outautomatically each time the system is initiated or as desired by acontrolling operator. The system operator can also execute a manualcalibration and verification of system performance. Isolating impedanceor isolation devices, generally Z, assist in insuring that there islittle “cross-talk” between input calibration signals. Required phaseand amplitude corrections for each frequency can be incorporated intothe processing by modifying the matrix K from which the signal vector isobtained in the signal vector equation.

Operator calibration can be carried out if the operator is uncertainabout the functioning of internal calibrator. FIG. 16 is a singlechannel microphone signal driver, generally 160, for providing anacoustic pressure wave reference to a standard signal. The system can becalibrated one microphone channel at a time, and includes a microphone162, an acoustically isolating microphone receptacle 164 having apressure wave channel 166, and a driving earphone/speaker 168.

FIG. 17 is a schematic representation of calibration device, generally170, which can feed identical simultaneous signals to each channel. Itcan be used to determine simultaneously the relative complexamplification of each acoustic channel, again circumventing the need forelectronically matched signal components, and includes a microphone 172,a driving earphone/speaker 174, a symmetric acoustic wave channelizer176, and an acoustically isolating microphone receptacle 178. In thecalibration devices shown in FIGS. 16 and 17, the acoustic signal feeddimensions should preferably be small in comparison to a wavelength.

FIG. 18 illustrates a composite seismic and acoustic system, generally180. Microphones 182 and/or geophones 184 can be simultaneously sampledas with two of the subsystems of the composite system 10 of FIG. 1. Acomputer 186 is preferably used as an array processor. This embodimentis useful as a multimode detection and tracking device and for rangedetermination, since seismic and acoustic waves typically have differingpropagation speeds.

FIG. 19 illustrates a schematic representation of a method of thepresent invention for remote calibration of microphone positions, and isuseful when antenna dimensions are large making position calibrationdifficult. Using a field survey device 192 transducer locations on anantenna 190 can be verified can be verified or recalibrated when thepositions have been altered by environmental events.

The following example is provided for illustrative purposes, and it isto be understood that the present invention is not to be limited orconstrained by such example, as the present invention could be practicedin a variety of other applications and configurations.

EXAMPLE

In a representative example using the present invention, a deployment ofa simple embodiment of the present invention was carried out to validatethe capability for locating sources of blast and shock waves in amountainous environment using the signal averaging technique. In onetest 7 elements of a 16 element spherical array were employed as a 3Dantenna operating in reduced horizontal mode, after a field validationverified a partially broken data cable. The utilized signal vectorlibrary then consisted only of a subset of the 3D library correspondingto incoming waves near parallel to the earth's surface.

The array was deployed on one side of a bent canyon having canyon wallgrades running from zero to 60 degrees, with numerous rock outcroppings,protrusions, and canyon twists and turns. The width of the canyon rangedfrom approximately 150 to 300 ft in the vicinity of the array at thearray altitude, as viewed in different directions. Three shooterpositions were employed, all along a N-S line, the first being on theopposite canyon wall at 179 meters along a line nearly parallel to thecanyon's average axis, the remaining 2 were 32 meters north and 76meters south of the antenna Targets for the shooters were spread along aline on the opposite canyon wall, from south to west. All shooters hadroughly the same elevation as the antenna array. All of the consequentblast and shock wave time series were processed using the signalaveraging technique discussed above and appropriate for short durationsingle events.

A total of 39 rifle firings were observed. With the temporal processingwindow centered on the blast or shock wave pulse, only 5 rifle firingsresulted in error estimates of shooter positions above 5 degrees, withthe array having a resolving power of approximately 53 degrees. All ofthese 5 were associated with one shooter position, the one directlynorth of the array and out of line of site from the array itself. Thatposition was characterized by the shooter shooting from along anirregular rock wall ridge line, generating numerous echoes. The maximaerror observed in this instance was 14 degrees. The overall meanabsolute bearing error was 3.3 degrees, with 15 of 39 within 2 degrees.A movement of the temporal window to place the blast and shock wavepulses nearer to the end of the window to reduce the effect ofreverberation reduced the maximum error to 8 degrees, and 1 to 2 degreefluctuations in other bearings were noted, characterizing the accuracyof the process. With the new temporal window, the overall error wasnearer 3.5 degrees, with two thirds of the shootings associated witherrors of 3 degrees or less. Use of high density arrays of the typeproposed here is anticipated to greatly enhance accuracy.

Identical processing results were obtained for the partial wave andFourier signal vector representations. In all cases, data processinginvolved 1 sec “snapshots” for data collection and 1 sec for processing.With use of an 18 element transducer array, the same acoustic “pulse”processing technique was found to generate valid results insidebuildings.

While preferred embodiments of the invention have been described usingspecific terms, such description is for present illustrative purposesonly, and it is to be understood that changes and variations to suchembodiments, including but not limited to the substitution of equivalentfeatures or parts, and the reversal of various features thereof, may bepracticed by those of ordinary skill in the art without departing fromthe spirit or scope of the following claims.

1. An apparatus for determining selected information from fluctuationsof a physical wave field, the properties of the physical wave fieldbeing detectable over three spatial dimensions and a temporal dimension,the apparatus comprising: at least one antenna having a neighborhood;said antenna being capable of generating output signals representativeof the physical wave field in said neighborhood; said output signalsbeing sufficient to define a signal vector characterizing the physicalwave field in said neighborhood; means for converting said outputsignals to said signal vector; and means for determining the selectedinformation from said signal vector.
 2. A method of determining selectedinformation from signals contributing to a physical wave field, theproperties of the physical wave field being detectable over threespatial dimensions and a temporal dimension, the method comprising:providing an antenna having a neighborhood; creating a signal vectorrepresentative of the physical wave field in said neighborhood; creatinga mathematical model of the physical wave field in said neighborhoodfrom said signal vector; and determining the selected information fromsaid mathematical model.
 3. A method for determining within a backgroundenvironment the presence of a source of a signal contributing to aphysical wave field, the properties of the physical wave field beingdetectable over tree spatial dimensions and a temporal dimension, themethod comprising: characterizing the physical wave field by a physicalwave field signal vector representing a mathematical model of thephysical wave field; providing a library of library signal vectorscharacterizing physical wave fields with known properties; determiningbackground signal vectors characterizing the background environment; anddetermining the presence of the source using at least one of saidbackground signal vectors, at least one of said library signal vectors,and said physical wave field signal vector.
 4. A method of determiningthe directions of a multiple sources contributing to a physical wavefield, the properties of the physical wave field being detectable overthree spatial dimensions and a temporal dimension, the methodcomprising: characterizing the physical wave field by a physical wavefield signal vector representing a mathematical model of the physicalwave field; providing a library of library signal vectors having libraryelements whose properties represent potential physical wave fields;using at least one of said library signal vectors and said physical wavefield signal vector to determine probable detections; resolving at leastone of the multiple sources using said probable detections; associatingat least one of said library signal vectors with each of said resolvedsources; and determining the direction of each said resolved sourceusing said at least one library signal vector associated with each saidresolved source.
 5. A method of determining selected information from aphysical wave field containing background interference from at least onesource contributing to a physical wave field, the wave field beingdetectable over three spatial dimensions and a temporal dimension, themethod comprising: characterizing the physical wave field by a physicalwave field signal vector representing a mathematical model of thephysical wave field; providing a library of library signal vectorscharacterizing physical wave fields with known properties; determiningbackground signal vectors characterizing the background interference;and determining the selected information using at least one of saidbackground signal vectors, at least one of said library signal vectors,and said physical wave field signal vector.
 6. A method of determiningthe direction of at least one source contributing to the physical wavefield containing background interference from a source contributing to aphysical wave field, the wave field being detectable over three spatialdimensions and a temporal dimension, the method comprising:characterizing the physical wave field by a physical wave field signalvector representing a mathematical model of the physical wave field;providing a library of library signal vectors characterizing physicalwave fields with known properties; determining background signal vectorscharacterizing the background interference; and determining thedirection of the source using at least one of said background signalvectors, at least one of said library signal vectors, and said physicalwave field signal vector.
 7. The method as defined in claim 6, furthercomprising: providing a directional map using said library signalvectors and said background signal vectors; and using said map in saiddetermining of the direction of the source.
 8. A method of constructingthe signals of resolvable sources contributing to a physical wave field,the properties of the physical wave field being detectable over threespatial dimensions and a temporal dimension, the method comprising:characterizing the physical wave field by a physical wave field signalvector representing a mathematical model of the physical wave field;providing a library of library signal vectors having library elementsrepresenting physical wave fields with known properties including thatof direction and frequency; using said library and said physical wavefield signal vector to assign directions to said resolvable sources andweights to said library elements associated with at least one of saidresolvable sources; and constructing the signal of said at least oneresolvable source using said library elements and said weights.
 9. Themethod as defined in claim 8, further comprising: summing Fouriertransforms of said library elements and producing a time series for saidat least one resolvable source; and manipulating said time series toobtain selected information.
 10. A method of calibrating a detection,tracking, and reconstruction system for signals contained in a physicalwave field, the method comprising: providing an antenna having multipletransducer defined channels; providing a library of library signalvectors having library elements representing physical wave fields withknown properties including that of direction and frequency; providingsignal conditioners associated with said channels; providing reversibletransducers that each provide a signal output and a calibrating signalinput; driving said reversible transducers with a common electricalsignal input, determining the relative amplitude and phase of saidsignal output of each of said channels; and modifying said signal vectorlibrary elements to compensate for amplitude and phase differencevariations between said channels in said signal conditioners and saidoutputs of said transducers.
 11. An antenna for use in an apparatus fordetermining selected information from fluctuations of a physical wavefield, the antenna having a neighborhood associated therewith and astructure portion, the antenna comprising: transducers that convert thefluctuations of the physical wave field into electrical signalsrepresentative of the fluctuations at predetermined positions; means forsampling said transducers according to Nyquist criteria; and saidtransducers being configured to allow sampling of said electricalsignals sufficient to construct a mathematical model of the physicalwave field in said neighborhood.
 12. A method for predicting the signaloutput of a transducer positioned in the neighborhood of an antenna,wherein the antenna includes transducers sampled and positioned forcompliance with temporal and spatial Nyquist criteria applied to asampled physical wave field, the method comprising: characterizing thephysical wave field by a physical wave field signal vector representingthe physical wave field; providing a library of library signal vectorshaving library elements representing physical wave fields with knownproperties; constructing a time series at the transducer positions usingsaid physical wave, field signal vector and at least one library signalvector; generating a mathematical model for said time series solution inthe neighborhood of the antenna; and using said mathematical model todetermine the signal to be detected by a transducer placed at a locationin the neighborhood of the antenna.
 13. A method of determining selectedinformation from signals contained in a physical wave field, theproperties of the physical wave field being detectable over threespatial dimensions and a temporal dimension, the method comprising:characterizing the physical wave field by a physical wave field modelingvector specifying a mathematical model of the physical wave field; anddetermining the selected information from said physical wave fieldmodeling vector.
 14. A method of determining the presence of a signalbelonging to a source contributing to a physical wave field, propertiesof the physical wave field being detectable over three spatialdimensions and a temporal dimension, the method comprising:characterizing the physical wave field by a physical wave field modelingvector specifying a mathematical model of the physical wave field; anddetermining the presence of a source using said physical wave field amodeling vector.
 15. An apparatus for determining selected informationfrom temporal fluctuations of a physical wave field, the properties ofthe physical wave field being detectable over three spatial dimensionsand a temporal dimension, the apparatus comprising: at least one antennacapable of generating output signals representative of the physical wavefield; said output signals being sufficient to define a physical wavefield modeling vector characterizing the physical wave field; means forconverting said output signals into at least one physical wave fieldmodeling vector; and means for determining the selected information fromsaid at least one physical wave field modeling vector.
 16. A method ofdetermining selected information from signals contained in a physicalwave field, the properties of the physical wave field being detectableover three spatial dimensions and a temporal dimension, the methodcomprising: creating a physical wave field modeling vectorrepresentative of the physical wave field; creating a mathematical modelof the physical wave field from said physical wave field modelingvector; and determining the selected information from said mathematicalmodel.
 17. A method for constructing an antenna structure for use indetermining selected information from a physical wave field, the antennastructure having transducers, and the antenna structure having aneighborhood associated therewith, the method comprising: providing amathematical model sufficient to substantially account for the effectsof the antenna structure on propagation of the physical wave field inthe neighborhood of the antenna structure, said model being sufficientto indicate placement of transducers on the antenna structure incompliance with Nyquist sampling criteria for the physical wave field inthe neighborhood of the antenna structure; and using said model todetermine placement of the transducers on the antenna structure.
 18. Amethod of providing signal vectors representing physical wave fields inthe neighborhood of an antenna structure, the method comprising:providing a mathematical model sufficient to substantially account forthe effects of the antenna structure on propagation of the physical wavefields in the neighborhood of the antenna structure, said model beingsufficient to indicate placement of transducers on the antenna structurein compliance with Nyquist sampling criteria for the physical wavefields in the neighborhood of the antenna structure; and using saidmodel to obtain sufficient information to construct signal vectorsrepresenting the physical wave fields in the neighborhood of the antennastructure.